[SOLVED] A modem, wireless router, and more wired ports

This is a discussion on [SOLVED] A modem, wireless router, and more wired ports within the Networking Support forums, part of the Tech Support Forum category. My latest wireless router just died so it's time for a new one.
I have a modem that has 4

I have a modem that has 4 ports, and I had one going to my wireless router and from the wireless router, I had 4 wired computers. <cable internet>

I added 3 more computers directly to the modem for a total of 7 computers via 2 devices (modem and wireless router- all connections wired).

Today I could not access the wireless router although the internet still worked. I reset the router and the internet stopped working on the computers connected to the wireless router even though the computers connected to the modem still worked fine.

Since it's almost undeniably broken, I want to do a few things-

The wireless router is in the basement and it is moldy, damp and nasty down there. I have wires coming up from the modem....can I use any wire to connect a wireless router to? I also have a few computers wired through the walls to the basement that still need a replacement in the same location where the wireless router was....Can I run 2 devices that split signal into more ethernet jacks?

I would like it to look like this-

Modem has one output to wireless router, one output to a non-wireless router type device from which I split off more wired computers, and then 2 wires going directly to computers.

What equipment can I use to accomplish this? Do I need 2 routers, or can I use a hub to split off the signal from the modem to get internet to 4 other computers?

1 wireless which I intend to run off the modem, and 1 wired which is also off the modem...... since the modem has 4 ports, will it be able to control the addresses or do I have to run the wireless modem off the wire-only router?

If your Modem has 4 ports, it is also a router . . when you add a router to a router it does not work . . You can either return the two routers and order a switch and an Wireless Access Point, or you can convert the two routers using this guide:

If your Modem has 4 ports, it is also a router . . when you add a router to a router it does not work . . You can either return the two routers and order a switch and an Wireless Access Point, or you can convert the two routers using this guide:

Can't cancel at this point, and it looks like money was unnecessarily spent.....The old wireless router was probably working, but the settings were altered when I reset it since I now realize that the modem is also a router.

The guide seems to make it easy, but when it comes to networks, it's never as easy as it looks.....I hope this is as problem free as the guide makes it out to be.